1. Magnetic Forces and Fields
Objective: TSW understand and apply the concepts of a magnetic fields and forces by predicting the path of a charged particle in a magnetic field.

2. A Magnetic Field is a property of space around a magnet causing a force on other magnets.
Every magnet has two poles, North and South.
Like poles repel and unlike poles attract.
Magnetic fields are produced by moving charge, such as current moving in a wire.
The Earth has a magnetic field.

3. The next two slides contain vocabulary and equations, you should commit them to memory

4. Vocabulary electromagnet
A magnet with a field produced by an electric current.
law of poles
Like poles repel each other and unlike poles attract.
magnetic domain
Cluster of magnetically aligned atoms.
magnetic field
The space around a magnet in which another magnet or moving charge
will experience a force.
mass spectrometer
A device which uses forces acting on charged particles moving a magnetic field and the resulting path of the particles to determine the relative masses of the charged particles.
right-hand rules
Used to find the magnetic field around a current-carrying wire or the
force acting on a wire or charge in a magnetic field.
solenoid
A long coil of wire in the shape of a helix (spiral); when current is passed through a solenoid it produces a magnetic field similar to a bar magnet.

5. Equations and symbols:
where
B = magnetic field (T)
FB = magnetic force (N)
q = charge (C)
v = speed or velocity of a charge (m/s)
θ = angle between the velocity of a moving charge and a magnetic field, or between the length of a current-carrying wire and a magnetic field
r = radius of path of a charge moving in a magnetic field, or radial distance from a current-carrying wire.
m = mass (kg)
I = current (A)
L = length of wire in a magnetic field (m)
μo = permeability constant
= 4π x 10-7 (T m) / A

6. Let’s Get Started!

7. By definition magnetic field lines go out of the north pole and into the south pole. Here is two dimensional representation of a the field lines around a bar magnet. A compass will always point in the direction of the magnetic field lines. (Toward the magnetic south.)

8. Magnetic Field due to two bar magnets:
Constant B S

9. The Earth has a magnetic field. We don’t really know why
The Earth has a magnetic field. We don’t really know why. The geographic north is the magnetic south. Solar particles get trapped in the Earth’s magnetic field causing the Aurora borealis (Northern Lights)

13. The Magnetic Force on a moving charge in an external magnetic field.
A moving charge creates a magnetic field, therefore it will experience a magnetic force as it moves through an external magnetic field.
The direction of the force is given by right-hand rule #1.
The magnitude of this force is given by the equation:
FB = magnetic force (N)
q = charge (C)
v = velocity (m/s)
B = magnetic field (Tesla)
θ = the angle between v and B
simulation

14. The direction is given by right-hand rule #1:
Fingers: Point in the direction of the field.
Thumb: Points in the direction of the charge velocity.
Palm of hand: Points in the direction of the force on a positive charge.
Back of hand: Points in the direction of the force on a negative charge. N S v B F B F
I or v

15. Example: A magnetic field is directed to the right
Example: A magnetic field is directed to the right. Predict the direction and magnitude of the magnetic force on the following charges moving through the field. B + v
Direction: Into the page.

16. Example: A magnetic field is directed to the right
Example: A magnetic field is directed to the right. Predict the direction and magnitude of the magnetic force on the following charges moving through the field. B + v

17. Example: A magnetic field is directed to the right
Example: A magnetic field is directed to the right. Predict the direction and magnitude of the magnetic force on the following charges moving through the field. B + v
40º
Direction: Into the page.

18. Example: A magnetic field is directed to the right
Example: A magnetic field is directed to the right. Predict the direction and magnitude of the magnetic force on the following charges moving through the field. B v -
Direction: Out of the page.

19. To draw field lines perpendicular to the page we will use the following representations:
A field going into the page will be represented with X’s
X X X X
Bin
• • • •
A field going out of the page will be represented with •’s
Bout

20. Bin + FB More Examples: X X X X X X X X X v
Direction: Upward toward the top of the page.

21. Bout • • • • • • • • • - FB More Examples: v
• • • • • • • • • - v FB
Direction: Left. Negative x direction.

22. • • • • • • • • •

23. X X X X X X X X X

24. Let’s predict the path of a moving charge in a magnetic field.

25. Bin r + FB More Examples: X X X X X X X X X v
The charge will follow a circular path with a constant speed.

26. Example 1
A proton enters a magnetic field B which is directed into the page. The proton has a charge +q and a velocity v which is directed to the right, and enters the magnetic field perpendicularly.
q = +1.6 x C
v = 4.0 x 106 m/s
B = 0.5 T
Determine
(a) the magnitude and direction of the initial force acting on the proton
(b) the subsequent path of the proton in the magnetic field
(c) the radius of the path of the proton
(d) the magnitude and direction of an electric field that would cause the proton to continue moving in a straight line. v B q

27. The force on a current carrying wire in a magnetic field.
A current carry wire has charge moving through it.
Each of the moving charges will experience a force due to the magnetic field
The individual magnetic forces on each charge will produce a net force on the entire wire.
The magnitude of the force is given by the equation below:

28. The direction is given by right-hand rule #1:
Fingers: Point in the direction of the field.
Thumb: Points in the direction of the current flow.
Palm of hand: Points in the direction of the force on a positive charge. N S I B F B F
I or v

29. X X X X X X X X X
Direction: Downward (-y direction) I FB

30. • • • • • • • • • FB
Direction: To the left (-x direction) I

31. Example 2: A wire carrying a 20A current and having a length of 0
Example 2: A wire carrying a 20A current and having a length of 0.10m is placed between the poles of two magnets as shown below. The magnetic field is uniform and has a value of 0.8T. Determine the magnitude and direction of the magnetic force acting on the wire. I N S

32. Example 2
A wire is bent into a square loop and placed completely in a magnetic field B = 1.2 T. Each side of the loop has a length of 0.1m and the current passing through the loop is 2.0 A. The loop and magnetic field is in the plane of the page.
(a) Find the magnitude of the initial force on
each side of the wire.
(b) Determine the initial net torque acting on the
loop. B I

33. Magnetic Fields produced by currents. Ampere’s Law
A current carry wire produces a magnetic field around itself.
The direction of this field is determined using right-hand rule #2.
The magnitude of the magnetic field is found using the equation below:

34. Right-hand Rule #2 I
current I
Magnetic Field B I r

35. Example3: Find the magnetic field midway between the two current carrying wires shown in the diagram. Will the wires attract or repel each other?
I = 2A
I = 3A
40cm

36. Topic 12 Electromagnetic Induction36

37. Electromagnetic induction is the process by which an emf (voltage) is produced in a wire by a changing magnetic flux.
Magnetic flux is the product of the magnetic field and the area through which the magnetic field passes.
Electromagnetic induction is the principle behind the electric generator.
The direction of the induced current due to the induced emf is governed by Lenz’s Law.

38. Here is a visual model of what we did in chapter 19:
Loop of wire
and in an
External
magnetic field
Output
Force
(wire moves)
Input
Current
Electric Motor

39. Here is a visual model of what we will do in chapter 20:
Loop of wire
in an
External
magnetic field
Input
Force
(move wire)
Output
Current
Generator

40. The next two slides contain vocabulary and equations, you should commit them to memory

41. Important Terms
alternating current - electric current that rapidly reverses its direction
electric generator - a device that uses electromagnetic induction to convert mechanical energy into electrical energy
electromagnetic induction - inducing a voltage in a conductor by changing the magnetic field around the conductor
induced current - the current produced by electromagnetic induction
induced emf - the voltage produced by electromagnetic induction
Faraday’s law of induction - law which states that a voltage can be induced in a conductor by changing the magnetic field around the conductor
Lenz’s law - the induced emf or current in a wire produces a magnetic flux which opposes the change in flux that produced it by electromagnetic induction
magnetic flux - the product of the magnetic field and the area through which the magnetic field lines pass.
motional emf - emf or voltage induced in a wire due to relative motion between the wire and a magnetic field

42. Equations, Symbols, and Units
where
ε = emf (voltage) induced by
electromagnetic induction (V)
v = relative speed between a conductor
and a magnetic field (m/s)
B = magnetic field (T)
L = length of a conductor in a magnetic
field (m)
I = current (A)
R = resistance (Ω)
Φ = magnetic flux (Tm2 = Weber=Wb)
A = area through which the flux is
passing (m2)
= angle between the direction of the
magnetic field and the area through
which it passes

43. Magnetic Flux
Consider a rectangular loop of wire of height L and width x which sits in a region of magnetic field of strength B. The magnetic field is directed into the page, as shown below: L w
The magnetic flux is given by the following equation:
Φ = The magnetic flux (Tm2 = Wb)
B = The magnetic field (T)
A = area of loop (m2)
Φ = angle between the field and the area

44. Faraday’s law states that an induced emf is produced by changing the flux, but how could the flux be changed?
Turn the field off or on.
Move the loop of wire out of the field
Rotate the loop to change the angle between the field and the area of the loop.

45. Here is Faraday’s Law in equation form:
Where
Є = The induced emf (voltage) (V)
ΔΦ = The change in flux (Wb)
Δt = The change in time (s)
N = number of loops.
*Note that an emf is only produced if the flux changes. The quicker the flux changes the larger the induced emf.

46. The induced emf in the wire will produce a current in the wire
The induced emf in the wire will produce a current in the wire. The magnitude of the induced current is found using Ohm’s Law:

47. It is helpful to use RHR#2 when using Lenz’s Law.
The direction of the induced current is found using Lenz’s Law (conservation of energy).
Lenz’s Law – The induced current in a wire produces a magnetic field such the flux of the produced magnetic field opposes the original change in flux. In simple terms the wire resists the change in flux and wants to go back to the way things were.
It is helpful to use RHR#2 when using Lenz’s Law.

48. Example 1: A circular loop of wire with a resistance of 0
Example 1: A circular loop of wire with a resistance of 0.5Ω and radius 30cm is placed in an external magnetic field of 0.2T. The magnetic field is turned off in .02 seconds.
Calculate the original flux of the loop.
Calculate the induced emf.
Calculate the current induced in the wire.
What direction does the induced current have?
What other way could the same emf be induced without turning the field off?
• • • •

49. Let’s do some examples predicting the induced current direction using Lenz’s Law

50. • • • • • • • • X X X X X X X X Bout decreasing flux
• • • •
• • • •
Bout decreasing flux
Bout increasing flux
CCW CW
X X X X
X X X X
Bin decreasing flux
Bin increasing flux
CCW CW

51. If you are really struggling applying Lenz’s Law, then memorize the following table:
decreasing
Increasing
B out
CCW CW
B in

52. Calculate the induced emf in the circuit.
Example 2: A circuit with a total resistance of R is made using a set of metal wires and a copper bar. The magnetic field is directed into the page as shown in the diagram. The bar starts on the left and is pulled to the right at a constant velocity.
Calculate the induced emf in the circuit.
Calculate the current induced in the wire.
What direction does the induced current have?
What is the magnitude and direction of the magnetic force that opposes the motion of the bar?
X X X X X X X v L

53. The last example led to the equation for the motional emf
The last example led to the equation for the motional emf. The motional emf is the voltage induced in a wire as it moves in an external magnetic field. The induced emf will produce a current in the wire, which will in turn result in a force that opposes the motion of the wire. You don’t get something for nothing.
Motional emf
Where
Є = The induced emf (V)
B = The external magnetic field (T)
L = The length of the wire (m)
v = The velocity of the wire (m/s)

54. Find the emf induced in the rod.
Example 3: A conducting rod of length 0.30 m and resistance 10.0 Ω moves with a speed of 2.0 m/s through a magnetic field of 0.20 T which is directed out of the page. v
B (out of the page) L
Find the emf induced in the rod.
Find the current in the rod and the direction it flows.
Find the power dissipated in the rod.
d) Find the magnetic force opposing the motion of the rod.

55. Example 4: A square loop of sides a = 0. 4 m, mass m = 1
Example 4: A square loop of sides a = 0.4 m, mass m = 1.5 kg, and resistance 5.0 Ω falls from rest from a height h = 1.0 m toward a uniform magnetic field B which is directed into the page as shown.
Determine the speed of the loop just before it enters the magnetic field.
As the loop enters the magnetic field, an emf ε and a current I is induced in the loop.
(b) Is the direction of the induced current in the loop clockwise or counterclockwise? Briefly explain how you arrived at your answer.
When the loop enters the magnetic field, it falls through with a constant velocity.
(c) Calculate the magnetic force necessary to keep the loop falling at a constant velocity.
(d) What is the magnitude of the magnetic field B necessary to keep the loop falling at a
constant velocity?
(e) Calculate the induced emf in the loop as it enters and exits the magnetic field. a B h

56. Electromagnetic induction
If a magnet is moved inside a coil an electric current is induced (produced) 56

57. Generator/dynamo
A generator works in this way by rotating a coil in a magnetic field (or rotating a magnet in a coil) 57

58. Motor = generator
If electric energy enters a motor it is changed into kinetic energy, but if kinetic energy is inputted (the motor is turned) electric energy is produced! 58

59. Can you copy this sentence into your books please.
The Motor Effect
When a current is placed in a magnetic field it will experience a force (provided the current is not parallel to the field). This is called the motor effect.
Can you copy this sentence into your books please. 59

60. Sample question
In this example, which way will the wire be pushed? (red is north on the magnets) 60

61. Sample question
In this example, which way will the wire be pushed? (red is north on the magnets)
Current
Field 61

62. Electromagnetic Induction
Imagine a wire moving with velocity v in a magnetic field B out of the page.
Wire moving with velocity v L v
Region of magnetic field B out of page 62

63. The electrons in the wire feel a force (the motor effect) which pushes the electrons to the right. This creates a potential difference in the wire.
Electrons pushed this way L v 63

64. ε = BLv
This means that a conducting wire of length L moving with speed v normally to a magnetic field B will have a e.m.f. of BLv across its ends. This is called a motional e.m.f.
Wire moving with velocity v L v
Region of magnetic field B out of page 64

65. Faraday’s Law 65

66. Faraday’s Law
Consider a magnet moving through a rectangular plane coil of wire. N A S 66

67. Faraday’s Law
A current is produced in the wire only when the magnet is moving. N A S 67

68. Faraday’s Law The faster the magnet moves, the bigger the current. A N68

69. Faraday’s Law The stronger the magnet, the bigger the current. A N S69

70. Faraday’s Law
The more turns on the coil (same area), the bigger the current. N A S 70

71. Faraday’s Law The bigger the area of the coil, the bigger the current.71

72. Faraday’s Law
If the movement is not perpendicular, the current is less. N S A 72

73. Magnetic Flux (Ф)
Imagine a loop of (plane) wire in a region where the magnetic filed (B) is constant. B 73

74. The magnetic flux (Ф) is defined as Ф = BAcosθ where A is the area of the loop and θ is the angle between the magnetic field direction and the direction normal (perpendicular) to the plane of the coil. B 74

75. B Ф = NBAcosθ in which case we call this the flux linkage.
If the loop has N turns, the flux is given by
Ф = NBAcosθ in which case we call this the flux linkage. B
The unit of flux is the Weber (Wb) (= 1 Tm2) 75

76. It can help to imagine the flux as the number of lines of magnetic field going through the area of the coil. We can increase the flux with a larger area, larger field, and keeping the loop perpendicular to the field. B 76

77. Faraday’s law (at last!)
As we seen, an e.m.f. is only induced when the field is changing. The induced e.m.f. is found using Faraday’s law, which uses the idea of flux. 77

78. Faraday’s law
The induced e.m.f. is equal to the (negative) rate of change of magnetic flux,
ε = -ΔФ/Δt 78

79. Example question
The magnetic field through a single loop of area 0.2 m2 is changing at a rate of 4 t.s-1. What is the induced e.m.f?
“Physics for the IB Diploma” K.A.Tsokos (Cambridge University Press) 79

80. Example question Ф = BAcosθ = BA E = ΔФ = ΔBA = 4 x 0.2 = 0.8 V Δt Δt
The magnetic field (perpendicular) through a single loop of area 0.2 m2 is changing at a rate of 4 t.s-1. What is the induced e.m.f?
Ф = BAcosθ = BA
E = ΔФ = ΔBA = 4 x 0.2 = 0.8 V
Δt Δt 80

81. Another example question!
There is a uniform magnetic filed B = 0.40 T out of the page. A rod of length L = 0.20 m is placed on a railing and pushed to the right at a constant speed of v = 0.60 m.s-1. What is the e.m.f. induced in the loop? v L 81

82. The area of the loop is decreasing, so the flux (BAcosθ) must be changing. In time Δt the rod will move a distance vΔt, so the area will decrease by an area of LvΔt v L
LvΔt 82

83. ε = ΔФ = BΔA = BLvΔt = BLv Δt Δt Δt E = 0.40 x 0.20 x 0.60 = 48 mV v L
An important result, you may be asked to do this! v L
LvΔt 83

84. Lenz’s Law
The induced current will be in such a direction as to oppose the change in magnetic flux that created the current
(If you think about it, this has to be so…….
Conservation of Energy) 84

85. Alternating current N S
A coil rotating in a magnetic field will produce an e.m.f. N S 85

86. Alternating current
The e.m.f. produced is sinusoidal (for constant rotation)
e.m.f. V 86

87. Slip ring commutator
To use this e.m.f. to produce a current the coil must be connected to an external circuit using a split-ring commutator.
Slip-rings
lamp 87

88. Increasing the generator frequency?
e.m.f. V 88

89. Root mean square voltage and current
It is useful to define an “average” current and voltage when talking about an a.c. supply. Unfortunately the average voltage and current is zero!
To help us we use the idea of root mean square voltage and current. 89

90. Root mean square voltage
e.m.f. V 90

91. Root mean square voltage
First we square the voltage to get a quantity that is positive during a whole cycle.
e.m.f. V 91

92. Root mean square voltage
Then we find the average of this positive quantity
e.m.f. V 92

93. Root mean square voltage
We then find the square root of this quantity.
e.m.f. V 93

94. Root mean square voltage
We then find the square root of this quantity.
e.m.f. V
This value is called the root mean square voltage 94

95. Root mean square voltage
We then find the square root of this quantity.
e.m.f. V
Emax
Erms = Emax/√2 95

96. Transformers What can you remember about transformers from last year?96

97. Transformers Vp Vs Np turns Ns turns Primary coil Secondary coil
Iron core
“Laminated” 97

98. Transformers How do they work? Vp Vs Np turns Ns turns Primary coil
Secondary coil
Iron core 98

99. An alternating current in the primary coil produces a changing magnetic field in the iron core.
Np turns Vp Vs
Ns turns
Primary coil
Secondary coil
Iron core 99

100. The changing magnetic field in the iron core induces a current in the secondary coil.
Np turns Vp Vs
Ns turns
Primary coil
Secondary coil
Iron core
100

101. Vp/Vs = Np/Ns and VpIp = VsIs
It can be shown using Faraday’s law that:
Vp/Vs = Np/Ns and VpIp = VsIs
Np turns Vp Vs
Ns turns
Primary coil
Secondary coil
Iron core
101

102. Power transmission Power dissipated = I2R
When current passes through a wire, the power dissipated (lost as heat) is equal to
P = VI across the wire
Since V = IR
Power dissipated = I2R
102

103. Power transmission Power dissipated = I2R
Since the loss of power depends on the square of the current, when transmitting energy over large distances it is important to keep the current as low as possible.
However, to transmit large quantities of energy we therefore must have a very high voltage.
103

104. Power transmission
Electricity is thus transmitted at very high voltages using step up transformers and then step down transformers.
220 V
Step-down
250,000 V
15,000 V
Step-up
Step-down
15,000 V
104

105. Dangerous?
105